EXAM 1 March 13, 1991 PS 208
If you need a constant not given here or do not understand
a problem, please ask me about it. No notes, books, etc. may
be used during this exam.
2 -19
g = 9.8 m/sec e = 1.6 x 10 C
9 2 2
1/(4 pi epsilon ) = 9.1 x 10 N m / C
0
-7
mu / (4 pi) = 10 T m/ A
0
-31
The mass of the electron is 9.11 x 10 kg.
1. [10 points]
(a). Describe a good way to reconstruct Coulomb's Law
without memorization. You need not have a technique for finding
the arbitrary form of the constant, and you may use anything
in the heading of this exam.
(b). Explain a good technique for determining
without memorization how to determine the constant in Gauss's
Law. You may assume that you know Coulomb's Law.
2. A charge of -3Q is at the origin of coordinates.
Where must a charge +Q be placed on the x axis if the combined
field is to be zero at a point x = +b on the axis?
3. A proton (mass m ) is shot out along the x
p
axis from the origin with a speed v . In
0
this region, there is a constant electric field of magnitude
^
E pointed in the -x direction. How far
from the origin does the proton get before it stops?
4 (From homework). A solid nonconducting sphere of radius
r has a total charge Q which is distributed according
0
to rho = br , where rho is the charge per
unit volume (charge density) and b is a constant. Determine
the electric field at all points inside the sphere. Notice
that rho cannot be taken out of radial integrations,
but is a constant with respect to angular integrations. [If
you have trouble with dV, write out the closest form you can
and box it so I will know what you are using.]